Our work deals with a theoretical analysis of an influence of a deviation from the sine condition of an optical system on the kinematics of aperture rays, which are transformed by this optical system. An exact formula for calculation of the value of the departure from the sine condition that has to be satisfied by an optical system to achieve a constant speed of transformed rays is derived. Approximate relations valid in the scope of the Seidel third-order aberrations theory are also derived and examples of optical systems that satisfy these conditions are presented. Obtained results are important for a design of scanning optical systems used, e.g., for distance measurements and laser systems for surface refinement of materials.
© 2009 Optical Society of America
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